Behavior analogous to a second order phase transition is observed for the
homogeneous cooling state of a heavy impurity particle in a granular fluid. The
order parameter ϕ is the ratio of impurity mean square velocity to that
of the fluid, with a conjugate field h proportional to the mass ratio. A
parameter β, measuring the fluid cooling rate relative to the
impurity--fluid collision rate, is the analogue of the inverse temperature. For
β<1 the fluid is ``normal'' with ϕ=0 at h=0, as in the case of a
system with elastic collisions. For β>1 an ``ordered'' state with ϕ=0 occurs at h=0, representing an extreme breakdown of equipartition.
Critical slowing and qualitative changes in the velocity distribution function
for the impurity particle near the transition are notedComment: 4 pages (4 figures included